# Time Series - Parameter Calibration

## Introduction

Any statistical or machine learning model has some parameters which greatly influence how the data is modeled. For example, ARIMA has p, d, q values. These parameters are to be decided such that the error between actual values and modeled values is minimum. Parameter calibration is said to be the most crucial and time-consuming task of model fitting. Hence, it is very essential for us to choose optimal parameters.

## Methods for Calibration of Parameters

There are various ways to calibrate parameters. This section talks about some of them in detail.

### Hit-and-try

One common way of calibrating models is hand calibration, where you start by visualizing the time-series and intuitively try some parameter values and change them over and over until you achieve a good enough fit. It requires a good understanding of the model we are trying. For ARIMA model, hand calibration is done with the help of auto-correlation plot for ‘p’ parameter, partial auto-correlation plot for ‘q’ parameter and ADF-test to confirm the stationarity of time-series and setting ‘d’ parameter. We will discuss all these in detail in the coming chapters.

### Grid Search

Another way of calibrating models is by grid search, which essentially means you try building a model for all possible combinations of parameters and select the one with minimum error. This is time-consuming and hence is useful when number of parameters to be calibrated and range of values they take are fewer as this involves multiple nested for loops.

### Genetic Algorithm

Genetic algorithm works on the biological principle that a good solution will eventually evolve to the most ‘optimal’ solution. It uses biological operations of mutation, cross-over and selection to finally reach to an optimal solution.

For further knowledge you can read about other parameter optimization techniques like Bayesian optimization and Swarm optimization.